The New Yorker magazine once had a cartoon showing a storefront office with the company name on the window: “None of Your Damn Business Inc.” If it were publicly traded, the corporation’s stock would be down this morning.

That’s because of Tuesday’s ruling by the Supreme Court in a case barely noticed amid the frenzy of interest in the arguments on same-sex marriage. The decision looks like a victory for personal privacy. But the beauty may prove to be skin deep.

The case arose after two Miami-Dade police escorted a drug-sniffing dog to Joelis Jardines’ front porch, where the dog signaled the presence of narcotics.

They got a warrant to search the house, where they found marijuana plants. Jardines contended the search violated the Fourth Amendment ban on unreasonable searches, and the Florida Supreme Court agreed. By a 5-4 vote, the U.S. Supreme Court upheld that ruling.

So far, so good. Unless they get a judge to issue a search warrant, the police may not tromp through your home looking for cannabis. Nor may they climb a ladder to peek in the window. Using dogs to detect something that can’t be detected by normal human senses is the equivalent of a physical search.

That should have been a slam dunk. In 2001, the justices ruled that law enforcement agents are not entitled to use a thermal imaging device to detect heat emissions from a home — which could betray the use of high-wattage lamps used to grow pot. The court said this is no more permissible than it would be to let cops employ a new technology that can see through walls.

“We think that obtaining by sense-enhancing technology any information regarding the interior of the home that could not otherwise have been obtained without physical intrusion into a constitutionally protected area constitutes a search — at least where (as here) the technology in question is not in general public use,” wrote Justice Antonin Scalia. You would think special sense-enhancing technology with four legs and a wet nose would likewise trample on privacy.

But for some reason Scalia, who wrote the court’s latest opinion as well, shied away from extending his impeccable logic. Instead, he said the dog-sniffing was out of line because it involved trespassing on private property. Once the officers ventured into the area owned by Jardines without his permission, the Fourth Amendment limited what they could do.

The trespass rationale worries Christopher Slobogin, who directs the Criminal Justice Program at Vanderbilt Law School. “If the next case involves a drug-sniffing dog smelling an apartment that abuts a public sidewalk, presumably Scalia would say there is no search because there is no trespass,” he says. “But the privacy invasion of the home would still be just as significant.” Plenty of urban residences are within a few feet of a sidewalk, making them vulnerable to an accusatory Labrador retriever.

Justice Elena Kagan agreed, in a concurring opinion. In her view, cops violate privacy rights “when they use trained canine assistants to reveal within the confines of the home what they could not otherwise have found there” — even if they do it from a public way.

Why does it matter? Because dogs are the least of the ways in which the government will eventually be able to monitor spaces that once afforded sanctuary to anyone who wants to be left the hell alone. Last year, the court said police needed a warrant to put a GPS tracking device on a man’s car because they “physically occupied private property” — the vehicle — “for the purpose of obtaining information.”

But the day is nigh when the government can use a tiny drone to follow a car day after day. That would not require a cop to put hands on someone’s personal property. But the information gathered would be no different. It’s hard to see why one would be barred by the Fourth Amendment and the other would not.

Even Scalia may grasp that. In the GPS case, he acknowledged, “It may be that achieving the same result through electronic means, without an accompanying trespass, is an unconstitutional invasion of privacy.” Still: May be?

A person’s right to keep others off his property was once a sturdy protection for privacy. But in an age of intrusive new surveillance tools, it could leave us all with nowhere to hide.